Equilibrium Diagrams

Code:

L.EMAT013

Acronym:

DE

Keywords
Classification	Keyword
OFICIAL	Science and Technology of Materials

Instance: 2022/2023 - 1S

Active?	Yes
Responsible unit:	Department of Metallurgical and Materials Engineering
Course/CS Responsible:	Bachelor in Materials Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EMAT	43	Syllabus	2	-	6	52	162

Teaching language

Portuguese

Objectives

Knowledge and understanding of Phase Equilibrium Diagrams are important to Materials Engineering since the properties of materials are controlled by the thermal history of the alloys. Phase Equilibrium Diagrams are the foundation for performing basic materials research in solidification, crystal growth, joining, solid-state reaction, phase transformation, oxidation, etc. On the other hand, a phase diagram also serves as a road map for materials design and process optimization since it is the starting point in manipulating the processing variables to achieve the desired microstructures.

This curricular unit aims to use Phase Equilibrium Diagrams to understand the phase transformations and the interpretation of the microstructural evolution of the alloys. Even if most phase equilibrium diagrams relate to equilibrium state and microstructure, they are also helpful to understand nonequilibrium structures, which are often more desirable than those of equilibrium states due to the properties values attained. Materials of interest range from single to multi-component systems. While binary equilibrium diagrams can adequately represent many industrial systems, ternary or higher-order diagrams are often necessary to understand more complex systems, like certain industrial alloys, slags, or ceramic materials.

Learning outcomes and competences

This curricular unit will prepare students to:
1) understand the scientific bases of Phase Equilibrium Diagrams;
2) know the relations between the composition, temperature and phases volume, being able to apply them to Phase Equilibrium Diagrams of different systems;
3) possess the understanding of how the microstructure is formed and how this structure influences materials properties;
4) use Phase Equilibrium Diagrams as a point of departure to establish the microstructural evolution of materials with temperature.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Recommended prerequisites: concepts learnt on the curricular units of Chemistry I and II, and Materials Engineering I and II.

Program

Introduction
Gibbs’ phase rule.

Unary phase diagrams
- Allotropy.

Binary phase diagrams
- Isomorphic systems;
- The lever rule;
- Invariant reactions: (eutectic, eutectoid, monotectic, peritectic, metatectic, peritectoide and sintetic);
- Congruent transformations;
- Complex binary systems.

Ternary phase diagrams
- The ternary space model;
- Tie lines and tie triangles;
- Isomorphic systems;
- Monovariant equilibria (eutectic and peritectic);
- Invariant equilibria (eutectic, quasi-peritectic, and peritectic);
- Intermediate phases (congruently and incongruently melting);
- Liquid immiscibility;
- Complex ternary systems.

Thermodynamic assessment
- Basic concepts;
- Main computational methods.

Mandatory literature

Rhines, Frederick N.; Phase Diagrams in Mettalurgy
D. R. F. West; Ternary equilibrium diagrams. ISBN: 0412493101
A. Prince; Alloy phase equilibria

Complementary Bibliography

Saunders, N.; Calphad. ISBN: 0-08-0421296
João Lopes Baptista, Rui Ferreira e Silva; Diagramas de fases. ISBN: 972-8021-72-0
Zhao Ji-Cheng 340; Methods for phase diagram determination. ISBN: 978-0-08-044629-5

Comments from the literature

In addition to the bibliography indicated, there will be placed in the contents of the course a set of presentations prepared by the teacher.

Teaching methods and learning activities

Short tutorials, followed by the presentation and discussion of several cases, mainly phase diagrams of industrial importance to improve the understanding of scientific concepts.
Students, in small groups, solve problems of phase diagram interpretation, structure development, and solidification paths. The teacher accompanies case studies to develop student skills in the analysis and resolution of engineering problems.

keywords

Technological sciences > Engineering > Materials engineering

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	52,00
Total:	162,00

Eligibility for exams

Not applicable.

Calculation formula of final grade

Final mark = 100% of the exam mark

Examinations or Special Assignments

Not applicable.

Internship work/project

Not applicable.

Special assessment (TE, DA, ...)

Exceptional cases will be assessed based on a closed book written exam.

Classification improvement

Students have to enrol after getting a passing grade.